Q38E - University Physics with Modern Physics

Question

Monochromatic light with wavelength 490 nm passes through a circular aperture, and a diffraction pattern is observed on a screen that is 1.20 m from the aperture. If the distance on the screen between the first and second dark rings is 1.65 mm, what is the diameter of the aperture?

Step-by-Step Solution

Answer

The diameter of the aperture is 0.359mm.

Step 1: Diffraction from a circular aperture

The difference in the angular radius of the first and second dark rings is

Step 2: Diameter of the aperture

The distance between the first and second dark rings on the screen is a small circular arc, with the distance between the aperture and the screen as the radius.

As a result, the angular radius difference between the first and second dark rings is;

Now solving for D, putting the values;

Hence, the diameter of the aperture is 0.359mm.